Information Geometry and Phase Transitions

Abstract

The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A non-interacting model has a flat geometry (R=0), while R diverges at the critical point of an interacting one. Here, the information geometry is studied for a number of solvable statistical-mechanical models.

arXiv comment6 pages with 1 figure

References in corpus (3)

• The Information Geometry of the Spherical Model
• The Information Geometry of the One-Dimensional Potts Model
• The Information Geometry of the Ising Model on Planar Random Graphs

Cited by in corpus (42)

• Geometrothermodynamics
• Geometrothermodynamics of black holes
• $P-V$ criticality and geometrothermodynamics of black holes with Born-Infeld type nonlinear electrodynamics
• Thermodynamic Geometry Of Charged Rotating BTZ Black Holes
• Geometrical method for thermal instability of nonlinearly charged BTZ Black Holes
• Thermodynamic Geometry of Deformed Bosons and Fermions
• Thermodynamic Geometry of Fractional Statistics
• Ruppeiner Geometry of Anyon Gas
• Nonperturbative Thermodynamic Geometry of Anyon Gas
• Information geometric methods for complexity
• Does the brain behave like a (complex) network? I. Dynamics
• The geometry of thermodynamics
• On Grover's Search Algorithm from a Quantum Information Geometry Viewpoint
• Nonconvexity of the relative entropy for Markov dynamics: A Fisher information approach
• Information geometry in quantum field theory: lessons from simple examples
• Thermodynamics and Thermodynamic geometry of Park black hole
• Geometric Algebra and Information Geometry for Quantum Computational Software
• Thermodynamics and computation during collective motion near criticality
• Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics
• Thermodynamics of bosons systems related to Dunkl differential-difference operators
• Thermodynamic geometry of a kagome Ising model in a magnetic field
• Perturbative Thermodynamic Geometry of Nonextensive Ideal Classical, Bose and Fermi Gases
• Geometrical aspects of a generalized statistical mechanics
• Geometrothermodynamics in Horava-Lifshitz gravity
• A unified thermodynamic picture of Hořava-Lifshitz black hole in arbitrary space time
• Stability and anyonic behavior of systems with M-statistics
• Thermodynamic Geometry of Reissener-Nordström-de Sitter black hole and its extremal case
• Scalar curvature of systems with fractal distribution functions
• Geometry of Quantum Group invariant systems
• Inferring couplings in networks across order-disorder phase transitions
• Thermodynamic Geometry of the Born-Infeld-anti-de Sitter black holes
• Information geometry of scaling expansions of non-exponentially growing configuration spaces
• Curvature of fluctuation geometry and its implications on Riemannian fluctuation theory
• Kählerian information geometry for signal processing
• Thermodynamic systems as bosonic strings
• Information geometry, simulation and complexity in Gaussian random fields
• AIMS:Average Information Matrix Splitting
• Fluctuation geometry: A counterpart approach of inference geometry
• Information Splitting for Big Data Analytics
• Universal scaling relation and criticality in metabolism and growth of Escherichia coli
• Latent geometry emerging from network-driven processes
• Machine learning methods for multimedia information retrieval